﻿Intelligence and Miscellaneous Articles. 157 



perature of combustion of a given mixture ; for it includes two mag- 

 nitudes which are equally unknown beforehand — the quantity burnt, 

 and the temperature. 



To determine these two magnitudes for a given mixture is the 

 problem which I have set myself, assuming the phenomenon of dis- 

 sociation to be known in all its details. Although this assumption 

 is far from having been realized, the solution of this problem pos- 

 sesses henceforth a certain amount of interest^inasmuch as it enables 

 us to account for the circumstances which may influence the tempe- 

 rature of combustion, and the direction of this influence. It will be 

 seen, moreover, that it suggests various means of studying dissocia- 

 tion experimentally. 



Let us take, in the first place, a mixture of equal equivalents of 

 oxygen and hydrogen ; let us call c the specific heat of the mixture, 

 c' that of atjueous vapour, and let k, at a given moment, be the frac- 

 tion of the mixture which is not yet burnt ; we then easily establish 

 the proportion 



[kc + (l-k)c']t = (l-k)3240, 



whence ,_ 3240 — c't /,x 



~~ 3240 + (c-c')t 



Taking t as the abscissa and k as the ordinate, this equation is 

 that of an hyperbola each point of which, in the part with positive 

 coordinates, represents one of the states through which the mixture 

 would successively pass if the combustion could become complete. 

 The ordinate defines the composition of the mixture, the abscissa 

 gives the temperature. 



On the other hand, let us consider aqueous vapour brought to a 

 gradually increasing temperature. Let u be the tension of dissocia- 

 tion at a given moment — that is to say, the fraction which has been 

 transformed into a mixture of chemical equivalents of oxygen and 

 hydrogen ; if we suppose the pressure constant, u will be a function 

 of the temperature alone, or 



w=/(0 (2) 



This equation will be that of a curve which will also represent the 

 successive states of the aqueous vapour. 



From the position of the points where the curves (1) and (2) inter- 

 sect the axis of the t's and the horizontal k= 1 , they must of necessity 

 intersect each other between these two lines. 



The point of intersection corresponds to a moment at which the 

 gaseous mass in combustion is identical in composition and tempe- 

 rature with dissociated water. Now this is in a state of equilibrium 

 which it is incapable of modifying of itself; this is therefore the case 

 with the gaseous mass ; that is to say, always supposing it in an en- 

 closure impermeable to heat, it must remain indefinitely in the same 

 state. Here, therefore, we have the stationary condition, and the 

 corresponding temperature is the actual temperature of combustion. 



